1

CHAPTER 1

INTRODUCTION

1.1 GENERAL OBJECTIVES

Liquids, liquid mixtures (multicomponent) and solutions have

found wider applications (Rowlinson and Swinton 1982; Acree 1984;

Prausnitz et al 1986) in chemical, textile, leather and nuclear industries. The

study and understanding of thermodynamic and transport properties of liquid

mixtures are more essential for their application in these industries.

Liquids in pure form have wide range of applications that includes

automotives, pharmaceuticals, agrochemicals etc. However, mixtures of pure

liquids (binary/ternary) have been preferred in a number of engineering and

scientific applications such as chemical industries, engineering design and for

subsequent operations, heat transfer, mass transfer and fluid flow.

Furthermore, mixing volume effects of mixtures received greater attention

from both theoretical as well as practical applications which include paints,

varnishes and printing ink industries. Thus the research work on pure liquids

and liquid mixtures are never ending. The intermolecular interactions in pure

liquids and binary/ternary mixtures are estimated by various physical methods

such as Infrared (IR), Raman Effect, Nuclear magnetic resonance (NMR),

Dielectric, Ultraviolet (UV) and Ultrasonic method. Among these, ultrasonic

method was found to be accurate and sensitive and used by many researchers

in the past, to elucidate molecular interactions in liquids and in binary/ternary

mixtures. Ultrasonics is an area of intense scientific and technological

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research. In view of its extensive scientific and engineering applications, it

has drawn attention of large cross section of students, teachers, researchers,

non-destructive testing (NDT) professionals, industrialists, technologists,

medical researchers, instrumentation engineers, software engineers, material

scientists and others. Ultrasound, a mechanical wave, which interacts with

matters with a variety of wave modes, longitudinal to several surface waves,

which is possible for diverse applications. Ultrasonics started from the basic

subject of sound in physics and now represents a vast field of its own with

several branches and sub-branches of scientific pursuit and technological

importance.

Basic measurements of ultrasonics, viz. attenuation and velocity,

have been applied in verifying physical theories, microstructural

characterization, mechanical property evaluation and others.

Prior to ultrasonic application to mixtures/solutions, the

spectroscopic and dielectric techniques were the only tool to study the nature

and strength of molecular interactions. However, application of ultrasonics

has made possible not only the evaluation of physico-chemical properties of

the mixtures/solutions but also more reliability on the interpretation of

molecular interactions. Due to low cost, easy operational procedure and

spontaneous results, the molecular interaction studies through ultrasonics

have gained importance all over the world (Raj et al 2007).

Van’t Hoff in 1887 began the investigations on the binary liquid

mixtures both theoretically and experimentally by applying the powerful

methods of thermodynamics to the solutions in a systematic manner. The

thermodynamical method is contributed in the reduction of all measurements

of the binary liquid mixtures in equilibrium.

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Thermodynamics is the study of energy; its transformations and its

relationship to the properties of matter. The two major objectives for the

thermodynamical properties of the binary liquid mixtures are:

(i) Describing the properties of component molecules when it is

in its equilibrium state (showing condition of no tendency to

change in its property).

(ii) Describing the processes when there is a relative change in

properties of matter and relating these changes to the energy

transfers in the form of interactions, which accompany them.

Sound speed is a thermodynamic function. Accurate

thermodynamic data on dilute electrolyte solutions are frequently needed.

Many other thermodynamic properties of electrolyte solutions are determined

from sound speed (Nozdrev 1963; Synder and Synder 1974). According to

Eyring and Kincaid (1938), molecules in the liquid state are loosely packed so

as to leave some free space among them. A sound wave is regarded as

traveling with gas kinetic velocity through this space and with infinite

velocity through the rest of the path. Lageman (1945) was the first to point

out the sound velocity approach for the quantitative estimation of the

interactions in liquids. In recent years, ultrasonic speed studies in many of the

aqueous, pure non-aqueous and mixed electrolytic solutions (Pandey et al

1989) led to new in sights into the process of ion and ion-solvent interactions.

One of the fascinating problems of mixed solvent systems is that of the

consequences of intermolecular interactions. This is of particular significance,

owing to the practical applications of mixed solvent systems for the study of

various physico-chemical investigations. Ultrasonic velocity studies in

conjunction with the density studies play a vital role in the investigation of

intermolecular interactions in mixed solvent systems (Syal et al 1996). The

ultrasonic velocity in a liquid mixture is mainly determined by its

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intermolecular properties (Jacobson 1952). Many investigators (Arrigo 1981;

Samatha et al 1998) have studied the propagation characteristics of ultrasonic

waves in liquid mixtures and utilized the data to understand intermolecular

interactions. A renewed interest in this subject arose recently (Bonney and

Davis 1990) from the need to identify candidate liquid binary systems

possessing low absorption and low velocity for applications in stimulated

Brillouin scattering experiments and to identify relatively high absorption

liquid systems, needed for antireflection applications in ultrasonic signaling.

The liquid mixture problem is expected to yield a new insight into

the liquid structure. In the recent years, considerable interest has been shown

in determining the ultrasonic velocity of binary liquid mixtures in the light of

understanding the molecular interactions involved in it (Reddy and Murthy

1995). Intermolecular interaction studies in liquid mixtures in the light of

physico-chemical properties have been a matter of great interest during the

last few decades (Stokes and Mills 1965; Eyring and John 1969; Marcus

1977; Krestov 1991).

Ultrasonic propagation parameters yield valuable information

regarding the behaviour of liquid binary systems because intramolecular and

intermolecular association, dipolar interactions, complex formation and

related structural changes affect the compressibility variations in the

ultrasonic velocity (Haribabu et al 1996). Ultrasonic methods find extensive

application owing to their ability of characterizing the physico-chemical

behaviour of liquid systems from velocity data (Prakash and Darbari 1988).

Thermodynamic studies in liquids and liquid mixtures play an important role

in understanding the nature of molecular interactions.

The size, shape and polarity of molecules play an important role in

molecular interactions. The interaction is characteristic of a class of liquids

showing pronounced structural properties (Prakash et al 1990).

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The knowledge of the structure and molecular interaction of liquid

mixtures is very important from fundamental and engineering point of view.

Fundamental thermodynamic and thermophysical properties are essential

sources of information necessary for a better understanding of the non-ideal

behaviour of complex systems because of physical and chemical effects,

which are caused by molecular interactions, intermolecular forces, etc., of

unlike molecules. From a practical point of view, these properties are

necessary for the development of thermodynamic models required in adequate

and optimized processes of the chemical, petrochemical, pharmaceutical and

other industries. In addition, extensive information about structural

phenomena of mixtures is of essential importance in the development of

theories of the liquid state and predictive methods (Djordjevic et al 2009).

The concentration and temperature dependence of acoustic and

volumetric properties of multicomponent liquid mixtures has proved to be an

useful indicator of the existence of significant effects resulting from

intermolecular interactions (Oswal et al 1998). Mixed solvents are frequently

used as media for many chemical, industrial and biological processes, because

they provide a wide range of desired properties (Nain 2008a). Studies on

thermodynamic and transport properties of binary liquid mixtures provide

information on the nature of interaction in the constituent binaries (Kadam

et al 2006). Temperature dependence of transport properties is of valuable

importance in understanding the molecular behaviour in binary liquid

mixtures (Sarma and Sarma 1995). Derived parameters from ultrasonic speed

measurements and the corresponding excess functions provide qualitative

information regarding the nature and strength of interactions in liquid

mixtures (Douhert et al 1997).

The ultrasonic studies are extensively carried out to measure the

thermodynamic properties and predict the intermolecular interactions of

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binary mixtures. The sound velocity is one of these physical properties that

help in understanding the nature of liquid state (Reddy and Reddy 1999).

1.2 OTHER’S WORK ON BINARY MIXTURES

Thus, from literature it is seen that, the works on the binary

mixtures have been reported by many workers by measuring the density,

ultrasonic speed and viscosity, and the nature and strength of the molecular

interactions between the unlike molecules.

For example, Kumar et al (2009) measured the densities and

studied the excess molar volumes in the binary mixtures of cyclopentane with

1-propanol, 1-pentanol and 1-heptanol and found negative variations (positive

for 1-propanol) suggesting the strong specific interactions between the unlike

molecules in all the binary mixtures at 298.15 and 308.15 K.

Subhash et al (2010) reported positive deviations in excess molar

volumes and compressibilities accounting the dominance of the dispersive

forces for the binary mixtures of decan-1-ol with 1,2-dichloroethane,

1,2-dibromoethane and 1,1,2,2-tetrachloroethane at 293.15 and 313.15 K at

atmospheric pressure. Wang and Tu (2009) have drawn breaking of the

hydrogen bonding interactions between 1,3-dioxolane + 1-propanol or +

2,2,4-triethylpentane binary mixtures at 298.15 and 308.15 K from the

positive values of excess molar volume. Parsa and Faraji (2009) accounted

strong interactions from the negative excess molar volume and positive excess

Gibbs free energy of activation for the binary mixtures of water with

1,2-propanediol and 2-pyrrolidone and weak interaction from the positive

excess molar volume and negative excess Gibbs free energy of activation for

the binary mixture of 2-pyrrolidone with 1,2-propanediol at 313.15 K.

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Jain et al (2009) have shown strong intermolecular association from

the positive deviations in viscosity and excess Gibbs free energy of activation

and negative variations in excess molar volume for the binary mixtures of

methanol with n-butylamine and di-n-butylamine at 303.15, 313.15 and

323.15 K. Pal and Gaba (2009) have reported negative deviations in

compressibilities (positive for 1-propoxy-2-propanol + 1-butanol) and

positive deviations in ultrasonic speed values for the binary mixtures of

1-methoxy-2-propanol, 1-ethoxy-2-propanol, 1-propoxy-2-propanol,

1-butoxy-2-propanol and 1-tert-butoxy-2-propanol with 1-butanol and

2-butanol accounting the presence of significant interactions at 298.15 K.

Wisniak et al (2005) have reported positive excess molar volume

values accounting for the weak interactions in the binary mixture of butyl

acrylate + ethyl acrylate at 298.15 K.

Peralta et al (2005) have given the formation of some complex

between the molecules of dimethyl sulfoxide and methacrylic acid, vinyl

acetate, butyl methacrylate and allyl methacrylate at 298.15 K from the

negative variations in the excess molar volume values. Herraez and Belda

(2006) have reported negative variations in the excess molar volumes for the

binary mixtures of water with ethanol, 1-propanol, 2-propanol, 1-butanol and

2-butanol to account for strong interaction. They have also identified the

presence of dispersive forces from the positive variations in the excess molar

volume values for the binary mixture of water with methanol at 298.15 K.

Atik and Lourddani (2006) have investigated the excess molar

volumes for the binary mixtures of ethanol with fluorobenzene and

α,α,α-trifluorotoluene and diisopropyl ether with fluorobenzene, ethanol and

α,α,α-trifluorotoluene at the temperature 298.15 K and the pressure 101 kPa

and found negative deviations in the excess values for all the binary mixtures

(except α,α,α-trifluorotoluene + ethanol) and suggested the formation of

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hydrogen bonding between the unlike molecules. Gurung and Roy (2006)

accounted strong intermolecular hydrogen bonding in the binary mixtures of

1,2-dimethoxyethane with methanol, ethanol, propan-1-ol, butan-1-ol, pentan-

1-ol, hexan-1-ol or octan-1-ol at 298.15 K from the negative deviations in

compressibilities and excess intermolecular free length and positive

deviations in ultrasonic speed and excess acoustic impedance values.

Wisniak et al (2007b) have reported negative variations in excess

molar volumes for the binary mixtures of styrene with ethylbenzene and ethyl

acrylate accounting for the presence of strong specific interactions and

positive excess molar volume values on the binary mixture of ethylbenzene

with ethyl acrylate accounting for the weak interactions between the unlike

molecules at 298.15 K.

Romero and Paez (2007) accounted solute solvent specific

interactions for the aqueous solutions of 1-butanol, 1,2-butanediol,

2,3 butanediol, 1,3-butanediol, 1,4-butanediol, 1,2,4-butanetriol and 1,2,3,4-

butanetetrol at 298.15 K from the excess molar volume studies which are

negative over the whole composition range and the negative partial molar

volumes. Nain (2007c) accounted the breaking of hydrogen bonding between

the participating component molecules of the binary mixtures of formamide

with 2-butanol, 1,3-butanediol and 1,4 butanediol from the positive excess

molar volume values while for formamide with 1-butanol binary mixture the

excess molar volume values show a sigmoid i.e. positive to negative at 293.15

and 318.15 K.

Iloukhani and Samiey (2007a) suggested the rupturing or stretching

of the hydrogen bonding of the self associated molecules of 1-heptanol by the

other components of the binary mixtures (tetrachloroethylene,

methylcyclohexane) from the positive trends in excess molar volume and

negative deviations in viscosity values. Mokate and Ddamba (2008) studied

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the variations of excess molar volumes of the binary mixtures of

difurylmethane with ethanol, propan-1-ol, butan-1-ol, pentan-1-ol and hexan-

1-ol at the temperature range of 288.15-308.15 K and found that the excess

values are negative over the whole composition range while it becomes

sigmoid and attains whole positive at the higher temperatures indicating the

rupture of the hydrogen bonds between the alkanol molecules at higher

temperatures.

Saleh et al (2002) observed a contraction in volume indicating the

presence of strong interactions in the binary mixtures of water with

dimethylsulfoxide, tetrahydrofuran and 1,4-dioxane at a temperature range of

303.15-323.15 K from the negative excess molar volume values.

Iloukhani and Zoorasana (2005) have determined the positive

excess molar volume values in the binary mixtures of dimethylcarbonate

with chloroethanes (1,2-dichloroethane, 1,1,1-trichloroethane and 1,1,2,2-

tetrachloroethane) or chloroethenes (trichloroethylene and

tetrachloroethylene) at 298.15 K and explained the predominance of the

dispersive forces in all the binary mixtures. However for dimethylcarbonate +

1,1,2,2-tetrachloroethane binary mixture, the negative excess molar volume,

indicates the formation of aggregates between the unlike molecules.

Ali et al (2007) observed negative deviations in isentropic

compressibility and excess intermolecular free length accounting the presence

of specific interactions for the binary mixtures of dimethylsulphoxide with

cyclohexane/ cyclohexylamine and positive deviations in isentropic

compressibility and excess intermolecular free length accounting weak

interactions for the binary mixture of dimethylsulphoxide with cyclohexanol

at 30 ºC. Thiyagarajan and Palaniappan (2007) studied the deviations in

isentropic compressibility and excess intermolecular free length in the binary

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mixtures of aniline with methanol, ethanol and 1-propanol at 303 K and

concluded the existence of strong interactions between the unlike molecules.

In addition to this, there are some research works on the binary

mixtures of esters (vinyl acetate, diethyl oxalate and dibutyl phthalate with

normal alkanols (ethanol, butan-1-ol, octan-1-ol and decan-1-ol) at 303.15 K

(Pan et al 2000), ethylbenzene + n-alkanol (Dewan et al 1988), cyclohexane

with benzene, n-hexane, n-decane and benzene with n-hexane (Pandey et al

1998), benzyl alcohol with monocyclic aromatics (Ali and Tariq 2006b),

formamide with ethanol, 1-propanol, 1,2-ethanediol and 1,2-propanediol

(Nain 2008b), 2-methoxyethanol + acetone (Kinart et al 2002), 1,4-dioxane +

ethane-1,2-diol (Skranc et al 1995), propionic acid with aniline,

N,N-dimethylaniline, pyridine (Solimo et al 1974), diethylene glycol

monomethyl ether with 1-alkanols (Dubey et al 2010), 1,8-cineole + 1-alkanol

(Alfaro et al 2010), styrene with m-, o-, or p-xylene (Ali and Nabi 2008),

dimethyl sulphoxide + ethanol (Ali et al 1999a), dimethyl sulphoxide +

propan-2-ol, propan-1,2-diol or propan-1,2,3-triol (Nain et al 1998),

2-propanol with hexadecane and squalane (Dubey and Sharma 2009),

dimethyl sulphoxide with chloro and nitro substituted aromatic hydrocarbons

(Syamala et al 2006a), dipropylene glycol dimethyl ether with 1-alkanols (Pal

and Gaba 2008b).

Ali et al (2003a) have obtained positive variations in excess molar

volume and negative deviations in viscosity, excess free energy of activation

and rheochore parameter accounting the dominance of dispersive forces in the

binary mixtures of N,N-dimethyl acetamide +1-hexanol/1-heptanol at 25, 30,

35, 40 and 45 ºC. Hawrylak et al (1998) have reported strong interactions

through the negative variations in excess molar volume and compressibility

values for the binary mixtures of butanediols with water. Further, they have

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evaluated the apparent and partial molar volumes and compressibilities and

analyzed the departure from ideal solution behaviour for the above mixtures.

Haribabu et al (1996) observed negative variations in the excess

molar volume, intermolecular free length and isentropic compressibility

values and positive deviations in ultrasonic speed values for the binary

mixtures of DMSO + o-chlorophenol / o-cresol and N,N-dimethyl formamide

+ o-chlorophenol / o-cresol binary mixtures at 30 ºC accounting strong

interactions between the participating components. Rajendran (1993) has

shown the formation of strong hydrogen bonding due to the charge transfer

complex in the binary mixtures of triethylamine + phenol / o-cresol using high

positive variations in excess internal pressure values and the weak interactions

taking place between the triethamine + ethanol / n-propanol / n-butanol binary

mixtures from the small positive excess internal pressure values at 303.15 K.

Nikam et al (2000c) utilized the negative ∆ks and LfE values accounting for the

complex formation between the aniline and alcohol molecules at 298.15 to

313.15 K.

Similarly, there are some works on the binary mixtures of:

propylene carbonate + six alcohols at 298.15 K (Francesconi and Comelli

1996), heptane + 1-pentanol / 1-hexanol / heptanol / 1-octanol / 1-decanol and

1-dodecanol at 298.15 and 308.15 K (Sastry and Dave 1996), n-heptane,

n-octane, n-nonane with chlorobenzene, nitrobenzene and benzonitrile at

313.15 K (Reddy et al 1982), ethyl chloroacetate + cyclohexanone, +

chlorobenzene, + bromobenzene or + benzyl alcohol at 298.15, 303.15 and

308.15 K (Nayak et al 2003), N-methylacetamide with ethylene glycol,

diethylene glycol, triethylene glycol, poly(ethylene glycol)-200 and

poly(ethylene glycol)-300 at 308.15 K (Naidu et al 2003), hexane with

1-chlorohexane between 293.15 and 333.15 K (Bolotnikov and Neruchev

2003).

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Nikam and Kharat (2003a) have reported negative excess molar

volumes and positive deviations in viscosity for N,N-dimethylformamide with

aniline and benzonitrile indicating the presence of strong specific interactions

at 298.15 to 313.15 K. Hasan et al (2006) have shown positive VmE and ∆ks

and negative ∆η values accounting the presence of weak interactions in the

binary mixtures of chloroform with pentan-1-ol, hexan-1-ol and heptan-1-ol at

303.15 and 313.15 K. Kadam et al (2006a) have also reported positive VmE

and ∆ks and negative ∆η values accounting the presence of weak interactions

in the binary mixtures of chloroform with propan-1-ol and butan-1-ol at

298.15 to 313.15 K. Yang et al (2008) have accounted specific interactions in

the binary mixtures of JP-10 with n-octane and n-decane through the negative

molar volume values at 293.15 to 313.15 K. Pal and Gaba (2008a) obtained

negative VmE and ∆ks values indicating the presence of strong interactions in

the binary mixtures of 2-(2-hexyloxyethoxy) ethanol with n-butylamine,

dibutylamine and tributylamine at 288.15 to 308.15 K. Awwad et al (2008)

have reported negative VmE and positive ∆η values indicating the presence of

strong interactions in the binary mixtures of N-acetomorpholine + alkanols in

the temperature range of 293.15 to 323.15 K.

Furthermore, some authors have reported their work on the binary

mixtures of N-methylmorpholine + 1-alkanols (Awwad 2008), 2-propanol +

benzyl alcohol, + 2-phenylethanol and benzyl alcohol + 2-phenylethanol (Yeh

and Tu 2007), tributyl phosphate with hexane and dodecane (Tian and Liu

2007), 2-methyl-1-propanol with hexane, octane and decane (Dubey and

Sharma 2007), isomeric butanediol + N-methyl-2-pyrrolidinone (Mehta et al

2009), hexan-1-ol with 1,2-dichloroethane, 1,2-dibromoethane and 1,1,2,2-

tetrachloroethane (Bhatia et al 2009), dichloromethane with aniline or

nitrobenzene (Su and Wang 2009).

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1.3 TYPES OF MOLECULAR INTERACTIONS

In liquid mixtures, the possible interactions are between like

molecules as well as unlike molecules. These interactions are of two types;

namely, long-range and short-range. The long-range interaction includes

electrostatic induction and dispersion forces, which arises without the overlap

of the electron clouds due to the closer approach of interacting molecules. On

the other hand, short-range interactions such as dipole-dipole, dipole-induced

dipole, charge transfer, complex formation and hydrogen bonding interactions

arise when the molecules come closer together, resulting in a significant

overlapping of electron clouds. The long-range interactions are highly

directional.

The formation of complexes in the liquid mixtures and solutions

can be studied through the intermolecular forces. In the case of an ideal liquid

mixture, there is a change in volume or enthalpy while mixing. When two or

more liquids are mixed, then the mixture is not ideal. Thus, the deviation from

the ideality is explained based on the molecular interactions between the

components of the liquid mixtures.

1.4 OBJECTIVES OF THE PRESENT THESIS

Thus, a detailed literature survey shows that no author has made

any attempt to relate the structural aspects of liquids belonging to the

homologous series with the variation of thermodynamical parameters.

Further, intermolecular interaction studies in binary mixtures of toluene and

2-methyl-2-propanol with liquids belonging to the homologous series of

nitriles and ketones have not been reported with due emphasis on the

influence of the structure of the molecules at temperature ranges 298.15 K to

308.15 K.

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Thus, this thesis highlights the influence of the structure of liquids

belonging to the homologous series of alcohols, acetates, nitriles and ketones

on the thermodynamic parameters for the first time in the literature.

Furthermore, this thesis contains the details of intermolecular interactions

taking place in the following binary mixtures.

Toluene + Acetonitrile

Toluene + Propionitrile

Toluene + Butyronitrile

2-Methyl-2-Propanol + Aceotnitrile

2-Methyl-2-Propanol + Propionitrile

2-Methyl-2-Propanol + Butyronitrile

Toluene + Acetone

Toluene + Ethyl methyl ketone

Toluene + Acetophenone

2-Methyl-2-Propanol + Acetone

2-Methyl-2-Propanol + Ethyl methyl ketone

2-Methyl-2-Propanol + Acetophenone

The molecular interactions have been studied and reported using

several volumetric excess parameters, compressibility excess parameters,

acoustic excess parameters and transport excess parameters. The effect of

temperature on the molecular interactions are duly considered and reported.

The purpose of choosing the liquids belonging to the homologous

series of nitriles and ketones are briefed below.

Acetonitrile is used as a polar solvent in the purification of

butadiene. With only modest toxicity, it is sometimes included in

formulations for nail polish remover. In more specialized applications, it is a

common solvent of choice for testing an unknown chemical reaction. It is

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polar (3.84 D) with a convenient liquid range. It dissolves a wide range of

compounds without complications due to its low acidity. For this reason, it is

widely used as a mobile phase in HPLC. Similarly, it is a popular solvent in

cyclic voltammetry because of its relatively high dielectric constant.

Acetonitrile is used in photographic industry, in the extraction and refining of

copper and byproduct, ammonium sulphate. Further, acetonitrile is used for

dying in textiles and in coating composition. Propionitrile is a clear liquid

with an etherial, sweet odor. Propionitrile is poisonous when heated to

decomposition, or by treatment with acids. Butyronitrile is a clear liquid that

is miscible with ethanol, diethyl ether and dimethylformamide. Butyronitrile

can be prepared by the controlled cyanation of n-butanol with ammonia at

300°C with Ni-Al2O3 catalysts.

Ketones have medicinal importance, because such investigations of

their dipolar behaviour are important for their use in different drugs.

Acetone, an aliphatic ketone, liquid find applications in

automotives, when added to the fuel tanks of the automotives in tiny amounts,

acetone aids in the vaporization of the gasoline or diesel, increasing fuel

efficiency, engine longevity, and performance -- as well as reducing

hydrocarbon emissions. Moreover, acetone is miscible with water, ethanol,

ether, etc., and itself serves as an important solvent. The most familiar

household uses of acetone are as the active ingredient in nail polish remover

and paint thinner. Acetone is also used to make plastic, fibers, drugs, and

other chemicals. In addition to being manufactured as a chemical, acetone is

also found naturally in the environment, including in small amounts in the

human body. Butanone (Ethyl methyl ketone, EMK) is used in paints and

other coatings because of its quick evaporating property. It dissolves many

substances and is used as a solvent in processes involving gums, resins,

cellulose acetate and nitrocellulose coatings and in vinyl films. It is also used

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in the synthetic rubber industry. It is used in manufacturing of plastics,

textiles, in the production of paraffin wax, and in household products such as

lacquer, varnishes, paint remover, a denaturing agent for denatured alcohol,

glues and as a cleaning agent. EMK is also used in dry erase markers as the

solvent of the erasable dye. It is used for synthesis of methyl ethyl ketone

peroxide, a catalyst for some polymerization reactions. It is highly flammable.

It is not considered as a large health threat. Butanone (EMK) occurs as a

natural product. It is made by some trees and found in some fruits and

vegetables in small amounts. It is also released to the air from car and truck

exhausts. Acetophenone, an aromatic ketone, is used as an intermediate for

pharmaceuticals, agrochemicals and other organic compounds. It also has

been used as a drug to induce sleep. It is used in tear gas (especially as the

form of chloro acetophenone) and warfare.

Toluene is a powerful solvent, hardly soluble in water, useful in

polymerization, synthesis of aromatic derivatives and other chemical

reactions, in the cleaning of polymer surfaces, electronic materials, etc. and

also used as blending of petrol, as a solvent for paints, resins and rubber, as a

starting material for benzyl derivatives, benzoic acid and benzaldehyde.

2-Methyl-2-Propanol (2M2P) is used in the manufacture of

flotation agents, perfumes, paint removers, methacrylate, food flavorings, also

it is used as a denaturant for ethanol, an octane booster in unleaded gasoline,

and as a cleaning agent and solvent for pharmaceuticals, waxes and lacquers.

1.5 RELATIONS USED FOR THE EVALUATION OF THE

THERMODYNAMIC AND TRANSPORT PROPERTIES

The various thermodynamic and transport parameters, which are

calculated (Ali et al 2001b; Rao et al 2005; Das and Jha 1994; Mishra et al

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2007) and reported in this thesis, from the measurement of ultrasonic speed,

density and viscosity for the binary mixtures are as follows:

Molar Volume, Vm

/2211 MxMxVm (1.1)

Free Volume, Vf

2/3/ kMuV f (1.2)

Isentropic Compressibility, ks

2

1u

k s (1.3)

Isothermal Compressibility, βT

3

4294

31071.1

uTT

(1.4)

Thermal expansion coefficient, α

410191.0 T (1.5)

Intermolecular Free Length, Lf

21uKL f (1.6)

Acoustic Impedance, Z

uZ (1.7)

Free Energy of Activation, ∆G*

hNVRTG m /ln* (1.8)

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Internal Pressure, πi

6/73/22/1 // MukbRTi (1.9)

where, x -is the mole fraction, M – is the molar mass, subscript 1 and 2 refer

to component 1 and component 2 respectively. ρ and u are the density and

ultrasonic speeds of the mixtures, k being a temperature independent constant

and has a value of 4.28 × 109, η is the viscosity of the mixtures, T being the

absolute temperature, K is Jacobson’s constant that depends on temperature

and is given by [K=(93.875 + 0.375 T) × 10-8], R is the universal gas constant,

h and N are the Planck’s constant and the Avogadro number respectively and

the value of b is taken as 2.

1.6 RELATIONS USED FOR THE EVALUATION OF EXCESS

FUNCTIONS

Excess Parameters

2211 YxYxYY E (1.10)

where Y represents Vm / Vf / βT / / Lf / Z / ΔG* or i

Deviation in Isentropic Compressibility

2211 ssss kxkxkk (1.11)

Deviation in Ultrasonic Speed

2211 uxuxuu (1.12)

Deviation in Viscosity

2211 xx (1.13)

Redlich-Kister Polynomial Equation (1948)

i

ii

E xAxxY )21()1( 1

4

011

(1.14)

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Standard Deviations σ (YE)

The values of Ai coefficients are evaluated by using least squares

method with all points weighed equally and the corresponding

standard deviations σ (YE) are calculated by using the relation

212

exp /)( jnYYY EEcal

E (1.15)

where n is the number of experimental data points and j is the number of Ai

coefficients considered. The values of EcalY are obtained from equation (1.14)

by using the best-fit values of Ai coefficients.

1.7 PARTIAL MOLAR PROPERTIES (PARTIAL MOLAR VOLUME AND PARTIAL MOLAR COMPRESSIBILITY)

The partial molar properties (partial molar volume and partial molar

compressibility), 1,mP of component 1 and 2,mP of component 2 in the binary

mixtures are calculated by using the following relations (Wang et al 2004;

Mehta et al 1997)

pTEE

m xPxPPP ,12*

11, / (1.16)

pTEE

m xPxPPP ,11*

22, / (1.17)

where P is Vm or Ks (= ksV); *1P and *

2P are the molar properties for pure

components, 1 and 2, respectively. Ks is the molar isentropic compressibility.

The derivative, pTE xP ,1/ in equations (1.16) and (1.17) was obtained by

differentiation of the equations (1.14), which leads to the following equations

for 1,mP and 2,mP

n

i

ii

n

i

iim xiAxxxAxPP

1

11

221

01

2211, 21221 (1.18)

20

n

i

ii

n

i

iim xiAxxxAxPP

1

112

21

01

2122, 21221 (1.19)

The excess partial molar properties, EmP 1, and E

mP 2, over the whole

composition range are calculated by using the following relations

11,1, PPP mEm (1.20)

22,2, PPP mEm (1.21)

Using the values of partial molar properties,

1,mP and

2,mP at

infinite dilution obtained from the equations (1.16) - (1.19), the excess partial

molar properties, EmP

1, and EmP

2, at infinite dilution are calculated by using the

equations (1.20) and (1.21) substituting EimP

, and

imP , in place of EimP , and

imP , , respectively.

1.8 APPARENT MOLAR PROPERTIES (APPARENT MOLAR

VOLUME AND APPARENT MOLAR COMPRESSIBILITY)

The apparent molar properties (apparent molar volume and

apparent molar compressibility) 1,P and 2,P of the two components of the

mixture, calculated by using the following relations (Pal et al 2008a;

Hawrylak et al 1998)

1*

11, / xPPP E (1.22)

2*

22, / xPPP E (1.23)

Equations (1.22) and (1.23) allow easy calculation of apparent

molar properties from the experimental EP ( EmV or E

sK ) values and

corresponding mole fractions. Using the linear regression of 1,P vs. x1 for

dilute solutions of component 1 in component 2 and 2,P vs. x2 for dilute

21

solution of component 2 in component 1, the values of limiting apparent (or

partial) molar properties,

1,P and

2,P at infinite dilution have been obtained.

These are also known as partial molar properties at infinite dilution,

represented as

1,mP and

2,mP earlier. The values of EP

1, and E

P

2, have been

calculated using following equations

*11,1, PPP

E

(1.24)

*22,2, PPP

E

(1.25)

1.9 ESTIMATION OF THEORETICAL ULTRASONIC SPEED

USING SCALED PARTICLE THEORY (SPT)

In recent years, many attempts have been made to study the

molecular interactions in pure and binary liquid mixtures and various equation

of state (Barker and Henderson 1997). Khasare (1991) developed an equation

of state for a fluid of hard-sphere mixture and found close agreement with

computer simulation results.

Liquid molecules may be assumed to have different shapes other

than spherical. The chemical structure of a liquid molecule is known but no

definite shape has been attached to a liquid molecule. If the intermolecular

interaction in binary mixture is weak, then molecules may retain the same

shape in the mixture but for strong interactions, constituent liquid molecules

may be distorted or deformed. The distortion is likely to occur in most of the

cases hence the shape of liquid molecule may be called as behavioural shape

in a particular mixture (Ghosh et al 2004).

In Scaled Particle Theory (SPT) (Reiss et al 1959) different shapes

(such as Sphere, Cube, Tetrahedral, Disc A, Disc B, Disc C and Disc D) of

the participating components are considered and when the participating

components have the correct shapes the theoretical ultrasonic speed estimated

22

based on this model will give values close to the experimental values. Thus,

in this thesis, theoretical ultrasonic speeds of the binary mixtures are

estimated by assigning the above said seven shapes to the participating

components and compared them with experimental speeds. When the

participating components have the correct shapes the theoretical ultrasonic

speed estimated based on this model will give values close to the

experimental values. Hence for a binary mixture, 7 × 7 combinations of the

different molecular shapes (i.e. 49 combinations of shapes) have been tried

for the participating components at a particular temperature. Only when the

participating molecules have particular shapes the theoretical values closely

agrees with experimental ultrasonic speeds that will be determined by

Chi-square fit ( 2 ) (Udny and Kendall 1987). By using 2 test, the best-fit

combination of shapes of the participating component of molecules is arrived

at. Chi- square test ( 2 ) can be used to test the goodness of fit, which enables

us to find whether the deviations of the theoretical values from the

experimental ones are due to chance or really due to the inadequacy of the

theory to fit the data.

For hard sphere molecules of diameter a, the virial equation of state

can be written as (Baxter 1971)

)(321 3 aga

Tkp

NBN

(1.26)

where N is number density and g(a) is the value of the radial distribution for

r just greater than a. From equation (1.26), it is noted that a complete

knowledge of g(r) is unnecessary for obtaining the pressure; rather it is

sufficient to obtain its value at r=a. It was this observation that led to the

development of Scaled Particle Theory (SPT) by Reiss et al (1959) and

Lebowitz et al (1965).

23

Consider a spherical region of radius r inside the liquid. Let ρG(r)

be the concentration of molecular centres just outside the sphere, when there

are no centres lying inside it. From macroscopic view point an empty

spherical cavity of radius r inside the liquid plays exactly the same role as a

hard sphere molecule of diameter, 2r-a. When r=a, the cavity behaves as a

typical molecule (and hence the name SPT) and G(a) = g(a). Hence, equation

(1.26) becomes

321 ( )3 N

N B

p a G ak T

(1.27)

Instead of calculating g(r), SPT is concerned with G(a). It can be

shown that for 0 < r < a/2,

1

3413 NG r r

, and for r > a/2 (1.28)

124N BG r k T R dr p dV dS

(1.29)

where, σ is the surface tension, S is the surface area and V is the volume.

Using equations (1.28) and (1.29), and the requirement that G(r)

and its first derivative be continuous at r=a/2, one can arrive at

2

31

1N B

pk T

(1.30)

where 6/3a (1.31)

Gibbsons (1969, 1970) and Boublik (1974) applied SPT to mixtures

of hard convex molecules (not necessarily spherical) and obtained

2 2

2 31

1 1 3 1N N

N B N N N

AB B Cpk T V V V

(1.32)

24

where ii RxA , ii SxB , 2ii RxC , iHiVxV

iHii VandSR , are respectively the mean radius of curvature, surface

area and volume of a molecule of species i , ix is the mole fraction.

With vp CC / , we have

2/ uddp T (1.33)

where u is the ultrasonic speed, ρ is molecular density in the mixture.

From equations (1.32) and (1.33),

4

22

322

2

)1(12

)1(1

N

N

N

N

N VCB

VAB

VRTMu

(1.34)

The above equation for pure liquids reduces to

2

22

2

11

)1(1

N

N

N VSR

VRTMu

(1.35)

Introducing the dimensionless shape parameter, HVSRX / and

NHV , equation (1.35) is rewritten as

4

2

2

2

111

X

RTMu

(1.36)

Solution to the above equation is obtained as (Khasare 1991)

122 LKK (1.37)

where 2/11 XLK and 2/ MuTRL .

Mean radius and the surface area of a molecule can be written as

25

3/1HYVR and

2RZS (1.38)

where Y and Z are the parameters related to the shape of the molecule. If the

molecule is assigned different shapes (Table 1.1), then the corresponding

values of X, Y and Z (Shape Parameters) can be calculated (Table 1.2).

Using the values of M and γ from literature and the experimental

ultrasonic speed u, the values of α can be calculated for pure liquids for

different shapes of the molecules with the help of equation (1.37).

Table 1.1 Molecular assignments for different shapes

Shape Size R S HV Sphere radius = a a 24 a 3/4 3a Cube side = l 4/3l 26 l 3l Tetrahedron side = l 2/2arctan3l 23l 3)12/2( l Discs radius = a and depth l Disc A l = a 4/)1( a 24 a 3a Disc B 4/al 4/)25.0( a 2/5 2a 4/3a Disc C 2/al 4/)50.0( a 23 a 2/3a Disc D 10/al 4/)10.0( a 5/11 2a 10/3a

Table 1.2 Shape parameters

Shape HVSRX / 3/ HVRY 2

/ RSZ

Sphere 3.0000 0.6204 12.5664 Cube 4.5000 0.7500 10.6666 Tetrahedron 6.7035 0.9303 8.3247 Disc A 4.1416 0.7070 11.7218 Disc B 8.4790 0.9190 10.9244 Disc C 5.4624 0.7832 11.3712 Disc D 16.5822 1.1920 10.5253

26

1.10 ESTIMATION OF THEORETICAL ULTRASONIC SPEED USING STANDARD RELATIONS

The theoretical evaluation of ultrasonic speed in liquid mixtures is

of considerable interest. The theoretical evaluation of sound velocity based on molecular models in liquid mixtures has been used to correlate the

experimental findings and to know the thermodynamics of the mixtures. The

comparison of theoretical and experimental results also provides better understanding about the validity of the various thermodynamic, empirical, semi-empirical and statistical theories.

The theories used to calculate the ultrasonic speed in the binary liquid mixtures reported in this work are as follows:

1) Nomoto’s relation (1958)

3

ii

ii

VxRx

u (1.39)

where 31

uVR

2) Vandeal and Vangeal Ideal Mixing relation (1969)

2

1

222

2211

12

1

2211

11

uMx

uMx

MxMxu (1.40)

3) Junjie’s relation (Dewan et al, 1988)

21

222

22211

11

21

2211

2211

uVx

uVx

MxMx

VxVxu

(1.41)

4) Impedance relation (Baluja et al, 2002)

ii

ii

xZx

u

(1.42)

27

5) Collision Factor Theory (1963, 1974, 1975)

mV

BSuu (1.43)

where xi is the mole fraction, u the ultrasonic velocity, M the molecular

weight, ρ the density and Vi the molar volume of the components of the

binary mixtures, u = 1600 m s-1, S is the collision factor and B is the

geometrical volume and is given by [B = (4/3)πNr3], where r is the molecular

radius, given by [r3=3b/(16πN)], (b is the van der Waal’s parameter)

respectively.